ultidimensional simulation of speed controlled induction...

International Journal on Electrical Engineering and Informatics - Volume 8, Number 2, June 2016

Мultidimensional Simulation of Speed Controlled Induction Electric

Drives with Matching Reducers and Transformers

Viktor Petrushin, Vladimir Vodichev, and Rostislav Yenoktaiev

Institute of Electromechanics and Energy Management of Odessa National Polytechnic

University, Odessa, Ukraine

[email protected], [email protected], [email protected]

Abstract: Operation of different induction motors as a part of controlled - speed electric drives,

which carry out the same engineering problem, taking into account turning on of such devices

as the transformer and the reducer is examined. A variability of parameters of equivalent

circuits of the motors, linked with a modification of magnitudes and frequencies of voltage

feeding the motors, and also with saturation of magnetic circuits and displacement of currents

in windings of rotors is considered. Comparison of motors characteristics in static and dynamic

regimes is carried out. Energy, weight, size and cost parameters are defined. The possibility of

sampling of the best alternative of the drive, both on the above-stated indexes, and at cost of

losses of active energy is justified. Modelling of a thermal state of motors in static and dynamic

regimes is carried out. The analysis of vibroacoustic performance of the motors is made at

operation in the certain circuit design of the electric drive on the given control range:

vibrational velocity and vibrational acceleration of a magnetic origin, vibrational velocity of a

mechanical origin (the radial and axial), ventilating and magnetic noise. Mechanical indexes

(rigidity of the shaft, strength of the shaft and dynamic weightlifting capacity of the bearing),

characterizing a mechanical state of an induction motor are observed and compared.

Keywords: the induction electric drive, an speed-controlled induction motor, the reducer, the

transformer

1. Introduction

Using of the controlled-speed electric drive (CED) in all industries and on a transport

allows rationally control technological processes at minimization of consumption of energy

resources. A variety of systems of induction CED are characterized by including in them of

such devices as reducers and transformers, and last can be switched on not only on an entry,

but also on an exit of the frequency converter. Using of these devices considerably changes

operating characteristics of the CED. The majority of papers is devoted to modelling of the

CED without such devices both in static and in dynamic regimes [1,2,3,4,5]. It is expedient to

model operations of the CED including these devices.

2. Statement of problem

For shaping of models of matching transformers and reducers it is necessary to introduce a

row of the initial data defining both functional properties, and mass, weight, dimensional and

cost indexes. Last give the chance to observe economic aspects of the CED. The functional

properties are: for the reducer - a gear ratio (ired), for the transformer - a transformation ratio

(ktr). For correctness of energy balance of the electric drive calculation using of efficiency

factor is required (red, tr).

Taking into account in the simulation reducers and transformers in static and dynamic

regimes a rotational speed (nmech), the torque on the drive mechanism (Мmech), power consumed

by the drive (PCED), efficiency of the drive (ηCED), power of the mechanism (Рmech) are defined.

Besides, it is obviously possible to count weight, dimensions and cost parameters of all the

CED at use of those or other considered components.

Received: June 27th

, 2015. Accepted: May 13rd

, 2016

DOI: 10.15676/ijeei.2016.8.2.3

268

mailto:[email protected]

mailto:%[email protected]

mailto:[email protected]

The expressions considering using of the reducer and the transformer in the CED by

consideration of a static conditions, look like:

, ,mech mech m red red

red

nn M M i

i (1)

1 1 1 11 1 1 ,CED c red trP P P P P (2)

, ,mech m red CED m c red trP P (3)

1

2 2

sα sβ

1( ) ( ) ( ) ,

2[ ]i t i t i t (4)

Where Мm- the torque on the motor shaft; Рm- the useful mechanical power on the shaft of

the motor; P1- a consumed active power of the motor; ηc- efficiency of the motor; ηc- efficiency

of the convertor; U1- primary voltage of the transformer; U2- secondary voltage of the

transformer.

The mathematical models (MM) used for examination of the transitive electromagnetic and

electromechanical processes in controlled induction motors, are grounded on systems of

nonlinear differential equations of equilibrium of voltage and currents in system of converted

coordinates[6,7,8,9].

,)()()()()()( ttxttxtdrtu

dt

drαMsαrssαsα (5)

,)()()()()()( ttxttxtdrtu

dt

drβMsβrssβsβ (6)

[ ( ) ( ) ( )[ ( ) ( )

( ) ( )],

rα r ред rβ r s rα

M sα

dpω i t r t d t x t t

dt

x t t

(7)

[ ( ) ( ) ( )[ ( ) ( )

( ) ( )],

rβ r ред rβ r s rβ

M sβ

dpω i t r t d t x t t

dt

x t t

(8)

1 3{ ( ) ( )[ ( ) ( ) ( ) ( )]

2

( ) },

r

M sβ rα rβ sα

c r ред

d pd t x t t t t t

dt J

M

(9)

Where Ψsα(t) , Ψsβ(t) , Ψrα(t) , Ψrβ(t)– magnetic flux linkages of the stator and rotor windings

of the motor, accordingly on axes α and β;ωr – an angular speed of the mechanism; р – poles

pairs number; J – the total moment of inertia of the drive redused to the shaft of the motor;

Мс(ωr) – dependence of a moment of resistance of the mechanism on an angular speed; rs ,

rr(t) , xs(t) , xr(t) , xM(t) – active and total reactive resistances of windings of the stator and rotor

and resistance of a mutual induction, and all of them, behind exclusion rs, vary on each

integration step; d(t) – an auxiliary variable d(t) = [xs(t)·xr(t) – (xМ(t))2]

-1; usα (t), usβ (t) –

instantaneous values of voltage on axes α and β which are defined by peak voltage

Um (depending on the law of the frequency control) and an angular position of the generalised

voltage vector φ1

1 1( ) ( ) cos( ), ( ) ( ) sin( ),sα m s mu t U t u t U t (10)

thus the system is supplemented with two more differential equations

1 1 1 1и ( ),

d dt

dt dt (11)

Where ω1 – angular speed, ε(t) – the dependence in time of angular accelerations of the

generalised voltage vector, defined with a drive velocity diagram.

Viktor Petrushin, et al.

269

The expressions linking instantaneous values of currents and magnetic linkages, look like the

following:

( ) ( ) ( ) ( ) ( ) ( ) ,

( ) ( ) ( ) ( ) ( ) ( ) ,

s r s M r

s r s M r

i t d t x t t x t t

i t d t x t t x t t

(12)

Where isα , isβ – stator currents on axes α and β. The root-mean– square current of the stator

1

2 2

sα sβ

1( ) ( ) ( ) ,

2[ ]i t i t i t (13)

A mathematical model constructed on the basis of the above describer differential

equations, allows calculating of rotation speed, currents in the phases windings,

electromagnetic torques, power losses.

In each of the equations take place non– linear coefficients such as engine parameters

varying in each operating point, including due to saturation phenomena of the magnetic system

and the displacement current in the rotor winding [10]. One of the approaches to dynamic

characteristics of controlled induction motors analysis involves a preliminary determination of

these coefficients for the required operating point of the control range. Therefore, to analyse

the transient mode steady-state modes calculations are carried out in order to obtain the values

of all the equivalent circuit parameters taking into account current displacement in the rotor

winding and the magnetic saturation for the required operating point of the control range. MM

of steady runs for this purpose are used. In the calculations of dynamic modes changes in each

step of the integration of the system are taken into account, i.e. at certain points, the transition

from one speed to another, the magnitude and frequency of the supply voltage in accordance

with the used law of frequency regulation, equivalent circuit parameters. During the loads of

fan and pulling type the load torque also changes, the value of which, corresponding to the

angular rotation frequency is determined by the load characteristic. Improving of the adequacy

of MM is provided by implementing of this approach.

The conventional active power consumed by the motor in dynamic regimes under condition of

a sinusoidal supply voltage can be calculated through virtual values of voltage and currents

(14)

Real consumed active power P1 more than the conventional total on magnitude of not

considered losses (in a magnetic circuit, additional, mechanical)

1 1 st base st add mech addP P P P P P . (15)

Shaft power of the motor can be defined through magnetic linkages and currents with use

of meaning of a rotational speed of a rotor

2

3

2r r r r r mech extra

pP I I P P

(16)

The efficiency instantaneous value is defined by a ratio of instantaneous values of useful

power on the shaft of the motor Р2 to consumed active power P1.

3. The results of investigation

During the modelling of the CED according to system approach principles joint

consideration of transformers, motors and loadings, and also reducers and matching

transformers [11] is necessary. On department of electrical machines of the Odessa national

polytechnic university software product DIMASDrive [12] is developed, allowing to realise

such model operation.

1

3

2s s s sP U I U I

Мultidimensional Simulation of Speed Controlled Induction Electric Drives

270

The CED with the transistor frequency converter with the autonomous invertor of voltage

and pulse– width regulating further is observed. The law of the frequency control U/f = const

was observed. Reviewed the draft load with the power of Рload= 35 kW with a peak

torque1500N•m. At the given stationary magnitude of a loading, a demanded control range

(30-250 rpm) in systems of the CED can be ensured by different motors, under condition of

using of reducers and transformers.

Three alternatives of the CED are observed at voltage of the main 400 V and a frequency of 60

Hz.

For direct- drive CED (Figure 1) is chosen the motor 4А355М12, working with the

frequency converter (Mitsubishi FR-A 540 L-G EC, 75 kg, c=0.98) [13].

Figure 1. The block diagram of the direct-drive CED

For the CED with the reducer (Figure 2) is chosen the motor 4А250М4, working with the

frequency converter (Mitsubishi FR-A 540 L-G EC, 75 kg, c=0.98)and the reducer (1ЦУ200,

135 kg, ηred=0.98, ired=6.3) [13,14].

For the CED with the transformer and the reducer (Figure 3) are chosen the motor 4А200L4,

the step- up transformer (510 kg, ηtr=0.98, ktr=0.8), the reducer (1Ц2У-200, 170 kg, ηred=0.98,

ired=10) and the transistor frequency converter (Mitsubishi FR-A 540 EC, 35 kg, c=0.98)

[13,14,15].

Figure 2. The block diagram of the CED with the reducer

Figure 3. The block diagram of the CED with the reducer and the transformer

Figure 4. A set of speed-torque characteristics


271

The adjusting characteristics representing dependences of a variation of electrical, energy

and thermal magnitudes from a rotating speed, can be gained at use of characteristic families,

including mechanical, at various parameters of regulating on which characteristics of the load

mechanism are superimposed. On Figure 4 the set of speed- torque characteristics and the

given loading, matching to the block diagram figured on Figure 3 is presented.

At such combination of speed–torque characteristics and loadings it is observed three bands

which are manifested on character of adjusting characteristics. Within each band the uniform

modification of speed-torque characteristics and a load line occurs.

On Figure 5, Figure 6 and Figure 7 adjusting characteristics of observed СED are

presented.

The analysis of a thermal state of an induction motor is one of the major problems at

examinations of any system the CED. To the problems linked with the analysis of a thermal

state of an induction motor and heat calculations, numerous papers [16, 17, 18, 19, 20, 21, 22]

are devoted.

The thermal state of an induction motor defines level of its operate reliability. The

admissible reheat temperature is restricted to a class of thermal classification of applied

insulations. The majority of premature fallings out of an induction motor is called by an

accelerated ageing of isolation of a winding of the stator owing to excessive heating. This

problem is especially actual for the induction motors operated in the CED as additional

excessive heating is caused

Figure 5. A modification of currents consumed by motors over the speed range: 1 СED without

the reducer, 2 СED with the reducer, 3 СED with the reducer and the transformer

Figure 6. Performances of efficiency of motors over the speed range: 1 СED without the

reducer, 2 СED with the reducer, 3 СED with the reducer and the transformer


272

by magnification of losses because of no sinusoidal current, and also a decline of a tap of heat

to an environment at lowering of a rotational speed of motors with a self-ventilation. Heating

of a concrete induction motor depends on ambient conditions, magnitude of losses in its

constructional devices, intensity of an abstracted heat from these devices. The magnitude of the

energy loss and intensity of cooling of controlled induction motors define such operation and

technology factors:

The aspect and parameters of the load mechanism (dependence of a torque of resistance on

velocity and a moment of inertia of mechanism) define level of load and accordingly a

degree of loses in the motor on a various rotational speed.

Mode of operation S1 - S8.

Modification of the electrical machine (enclosed, protected, unclosed), ventilation system

(axial, the radial, immixed), a cooling aspect (independent, self-cooling), defining intensity

of heat removal from motor to an environment.

At an induction motor heat calculation should be considered not only a modification of

magnitude of a loading, but also parameters of the voltage feeding the motor gained from the

semiconductor convertor (SC) (frequencies, magnitudes, a spectral distribution). Last

parameters appreciably influence to allocation of losses in active parts and a common thermal

state of an induction motor. These parameters depend on structure of the main circuit of the

convertor, an aspect of regulating and the law of the control used in it.

In a heat calculation the problem of definition of excess of temperatures of various parts of

electrical machine over cooling environment temperature is put. Calculation should be made

with use of the geometrical dimensions and physical parameters of induction motors and

information about losses in various parts of the motor, gained as a result of electromagnetic

calculation of the motor. An important feature of controlled induction motor is its operation in

a various operating points of a control range. Therefore at thermo analysis the calculations of

the steady state thermal conditions occurring at long lasting operation in any operating point

are necessary, and also an unsteady thermal conditions at the dynamic transients linked with

regulating, starting, a deceleration and reverse of drive.

In practice of research and design of induction motors are applied various computational

methods of the steady state and unsteady thermal processes: a method of the equivalent heating

losses, an analytical method or a temperature pattern method, a method of the equivalent

thermal equivalent circuits (ETС). To the analysis of a thermal state of controlled induction

motors can be applied a simplified heat calculation by the method of heating losses and

calculation by means of ETС.

Method of EТС is well enough approved in practice of design of series of induction motors.

It is grounded on well-designed theory of electrical and thermal circuits and allows to define

medial temperatures of parts of a motor. To virtues of this method refer to use possibility at

various designs of motors, a possibility of raise of precision of account for the score of

magnification of number of devices of an equivalent circuit and refinement of meanings of

thermal conductances. Its application for calculation of temperatures of constructive elements

of the controlled induction motor should be performed taking into account specificity of

operation of the motor in the drive. At calculation following simplifications are accepted: the

cage rotor is considered as one device, cooling of end faces of cores of the stator and rotor is

not considered, machine cooling symmetrically and uniformly in a cross-section, thermal

conductances are independent of temperature. At development of mathematical model of a

thermal state of the motor a variety of constructive solutions of controlled induction motor

should be considered. It is necessary to provide a possibility of a heat calculation of motors

enclosed (IP44, IP54) and protected (IP22, IP23) modifications both with forced, and with self-

cooling with use in system of ventilation of axial and radial ventilating ducts. It is developed

EТС for heat calculations of nonstationary behaviours of controlled induction motors of the

enclosed modification (IP44, IP54) which is presented on figure 7 in which some conductances

at regulating vary and in the thermal circuit design they are marked out as variables. EТС for

heat calculations in a steady conditions will be converted at exclusion of the devices which are


273

representing heat capacities. The mathematical description in appropriate way changes.

Calculation of variable conductances is necessary for executing for each operating point. The

thermal conductances which have been marked out as variables by a dot line, vary at self-

cooling and remain invariable at a dusting the independent ventilating fan. In a heat calculation

the problem of definition of excess of temperatures (excessive heating) of various constructive

parts of the electrical car over ambient temperature is solved. Constructive parts of the

electrical machine possess certain heat capacities which values depend on used materials and

their geometrical sizes.

At the solution of a problem of definition of excess of temperatures of various constructive

parts of the electrical machine over environment temperature in an observed equivalent circuit

of substitution following constructive parts of an induction motor are introduced:

1. The stator core (fingers and a back) with medial superheat temperature 1, heat capacity С1

and power losses Р1 (magnetic losses in the core taking into account the additional iron

loss of the stator).

2. The short-circuited cage of a rotor and fingers of a rotor with medial superheat temperature

2, heat capacity С2and power losses Р2 (the total of losses of rotor bars, short-circuited

rings and the additional losses in fingers and a rotor winding).

3. The grooving part of a winding of the stator with medial superheat temperature 3, heat

capacity С3 and power lossesР3.

4. Front parts of a winding of the stator with medial reheat temperature 4, heat capacity С4

and power losses

4 1 3elP P P .

5. Interior air (IA) with medial temperature 5, heat capacity С5and interior ventilating losses

Р5.

6. The frame with medial superheat temperature 6, heat capacity С6.

7. End shells with medial temperature 7, heat capacity С7.

8. In EТС following thermal conductances are presented:

Figure 7. The equivalent thermal equivalent circuit of controlled induction motor of the

enclosed modification (IP44, IP54) for the analysis of unsteady thermal processes

1 – conductance between a package of the stator and a cooling environment at unpackaged

modification.

1.2 – conductance of a stator-to-rotor gap between the core of the stator and a rotor.

ΔP4

ΔP2

Λ2 C2

ΔP1

Λ1 C1

ΔP3 C3

Λ1.3

Λ3.4

C4

Λ1.6 Λ3.5

Λ5.6

Λ4.5

Λ6.7 Λ5.7

C7

Λ7.0 Λ6.0 C6

Λ1.2

Λ2.5.1

Λ2.52

Λ1.5

ΔP5

C5

Λ5


274

1.3 – shunt conductance of a grooving part of a winding from winding copper to the stator

core.

1.5=rvds+avds+surf – conductance from a stator package to IA, consists of conductances:

rvds the radial, avds axial ventilating ducts of the stator, surf surfaces of the core of the stator

to IA.

1.6 – conductance from a stator package to the frame (for the enclosed induction motors).

2– conductance from a rotor to chilling air (a scavenged rotor).

Λ2.5.1 – conductance from front parts of the squirrel cage to IA

Λ2.5.2 = rvdr+avdr+shaft – conductance from the rotor core to interior air, consists of

conductances rvdr the radial, avdr axial ventilating ducts of a rotor to IA, shaft conductance of

a rotor to IA through the shaft.

3.4 – axial thermal conductance of a winding of the stator.

3.5 – conductance from a grooving part of a winding of the stator to IA through the radial

channels.

4.5 – conductance from front parts of a winding of the stator to IA

5– the equivalent conductance considering heating of a cooling medium (for the protected

motors).

5.6 – conductance from IA to the blown frame.

5.7 – conductance from IA to the bearing shields.

6.7– conductance between the frame and bearing shields.

6.0 – conductance from a frame surface to chilling air.

7.0 – conductance from bearing shields to chilling air.

On the basis of offered universal EТС the system of differential equations of a heat account can

be made. In a matrix aspect the system is represented expression:

1

θ Δ θd

C P Λdt

,

Where – a matrix-column of medial excessive heating over temperature of a cooling

medium,

1

2

n

θ

θ

θ

; (17)

C – a matrix of heat capacities of matching constructive devices into which the induction motor

is conventionally dissected

1

2

0 0

0 0

0 0 n

C

CC

C

; (18)

– a matrix of thermal conductance

1 1 1 2 1

2 1 2 2 2

1 2

, , ,

, , ,

, ,

n

n

n,nn n

Λ Λ Λ

Λ Λ Λ

Λ Λ Λ

, (19)


275

Where Λ1,1Λ1,2…,Λп,п – thermal conductances between motor devices;

ΔP – a matrix-column of Joule heat losses in matching constructive devices of the electrical

machine

1

2

Δ

ΔΔ

Δ n

P

PP

P

. (20)

The solution of this first order system, for example by a Runge- Kutt method, allows to

observe a modification of temperatures of constructive devices of an induction motor at

transients. Adequacy in MM essentially rises at the account of modifications on each

integration step of losses.

Figure 8 shows the calculated temperatures of excessive heating of windings of motors stators

θс of observed CED for continuous operation within the control range.

Figure 8. A modification of temperatures of stator windings of motors over the control range:

1 CED without the reducer, 2 CED with the reducer, 3 CED with the reducer and the

transformer

The average for the control range design criteria [19] should reflect energy characteristics

of CAM in all control range from n1 to n2 and are defined as equivalent averaged for this range.

The same applies to the generalized criterion of reduced expenditures of the motor which

considers cost of manufacture and an expenditure for maintenance. Because expenditures

depend on efficiency and a power factor, the generalised criterion of reduced expenditures has

various meanings in different points of a control range and it is advisable to determine the

equivalent average value of this criterion for the entire control range.

If the control range energy indicators are calculated as the average for the entire range

2

12 1

1( ) ,

n

aAD АD

n

n dnn n

2

1

1 12 1

1cos cos ( ) ,

n

aАD АD

n

n dnn n

(21)

then a range criteria of given annual cost of the motor can be determined based on the

following. When you know the full cost of the engine ced criterion value is defined as

( )[1 ( )] ,АD rpc s de s АDRC ced C Т k k СL (22)

where rpcC -cost of expenditures for a reactive power compensation, UAH; АDСL -cost of

losses of the electric energy for a year, UAH; sТ - standard pay-back period of the motor,


276

years; dek - a share of expenditures for depreciation expenses; sk - a share of expenditures for

service at motor maintenance.

For controlled induction motors numerical value 5sТ years, 0.065dek , 0.069sk are

accepted the same, as for common industrial induction motors. Then

1.67( ) ,АD rpc АDRC ced C СL 1 1( – 0.484),rpc creС С P tg (23)

1 (1.04 ), АD cae АД АDСL С P (24)

where caeC - the coefficient considering cost of losses of active energy, representing product of

cost 1 кW·h the electric power during life expectancy of the motor (C = 0.13 c.u. for

кWh), the number of engine operating hours during the year (Tyear = 2100), number of years

of operation before big repair (5) and coefficient of relative motor load (КL =0.8), creС - the

coefficient considering cost of compensation of a reactive energy and representing product of

cost 1 kilovar of a reactive power of compensating devices (10 c.u. for 1 kilovar), coefficient of

participation of the motor in a peak load of the system (0.25).

2

12 1

1( ) .

n

aАD АD

n

RC RC n dnn n

(25)

It is necessary to note that at operation the CAM as a part of up-to-date variable-frequency

electric drives because of proximity of a power factor of the drive to 1 a component matching

to cost of compensation of a reactive energy may be excluded from expression of measure RC

of the electric drive

[1 ( )] ,CED s de s CEDRC ceр Т k k СL (26)

where ceр - an overall cost of the electric drive,

1 (1.04 ).CED cae CED CEDС С P

Numerical values of the coefficients, costs, hours and years are used same, as for definition

АDRC

2

12 1

1( ) .

n

aCED CED

n

RC RC n dnn n

(27)

Table 1 shows the values of parameters considered CED to which number refer to medial

band efficiency (η) and reduced expenditures (RC), and also mass, dimensional and cost

indexes of motors and drives are resulted.

Account of cost of losses of active energy for year can be executed

1 0.04 ) / ,(year L mechae CED CEDCL C T K P (28)

Where 0.04 - the relative magnitude of losses in a user supply net.

Comparison of the observed alternatives the CED at cost of losses of active energy for a

year (Table 2) is executed.

Comparison of the observed alternatives the CED at cost of losses of active energy for a

year (Table 2) is executed.

Modelling for each circuit solution of the CED is also executed at operation on set

tachogram (starting 1.5 s to 150 rev/min, 1 s – 185 rev/min) taking into account transients.

On Figure 9, Figure 10, Figure 11 and Figure 12 the versus time graphs gained at modelling of

operation observed CED on set tachogram are presented.


277

Excessive heating characteristics display that at each step of tachogram two sections are

observed. First matches to the transitive electromechanical process, second - to heat on an

exhibitor with a trend of reaching of final values of superheat temperature.

Excessive heating characteristics display that at each step of tachogram two sections are

observed. First matches to the transitive electromechanical process, second - to heat on an

exhibitor with a trend of reaching of final values of superheat temperature.

Table 1. Comparison of various CED indexes

Indexes and

parameters

CED

Without the reducer

and the transformer

CED

With the reducer

CED

With the reducer

and the transformer

η Motor, % 88 93.55 90.34

cosφ Motor, r.u. 0.76 0.89 0.64

η CED, % 86.31 89.9 85.23

RC Motor, c.u. 102926 10908 44690

RC CED, c.u. 205991 108381 118600

Mass Motor, kg 1670 560 325

Volume

Motor, dm3 161.7 75.6 34

Value Motor, c.u. 18039 5437 3294

Mass CED, kg 1745 770 1040

Volume CED, dm3 290.7 255.6 666

Value CED, c.u. 75039 63437 38762

Figure 9. Characteristics of a rotational speed of the mechanism: 1 CED without the reducer, 2

CED with the reducer, 3 CED with the reducer and the transformer.

Figure 10. Characteristics of currents consumed by motors: 1 CED without the reducer, 2 CED

with the reducer, 3 CED with the reducer and the transformer


278

Table 2. Comparison of costs of losses of active energy for various CED

Indexes and

parameters

CED

Without the reducer

and the transformer

CED

With the reducer

CED

With the reducer and

the transformer

η CED, % 86.31 89.9 85.23

Value CED, c.u. 1299 993.36 1398

Forces of a magnetic, mechanical and aerodynamic origin cause vibration and noise of

electrical machines. Magnetic sources of vibration and noise are bound to the higher space and

time harmonics of a magnetic field which are caused by presence of fingers on the stator and

on a rotor, polyharmonic composition of a supply voltage, a stator-to-rotor gap eccentricity,

nonsinusoidal allocation of MMF of a winding, saturation of the magnetic circuit of the

machine and a row of other causes. Mechanical causes are lack of balance a rotor,

misalignment and a distortion of mounting faces of the bearing, an aberration in the form of

their rings and spread of sizes of a separator, a thermal strain of a rotor, a shaft bending flexure

etc. The aerodynamic noise is formed by the ventilating fan and other details had on a rotor.

Vibrations and induction motor noise were observed by many authors [23, 24, 25].

Figure 11. Characteristics of efficiency of motors: 1 CED without the reducer, 2 CED with the

reducer, 3 CED with the reducer and the transformer

Figure 12. Characteristics of excessive heating of windings of stators of motors: 1 CED

without the reducer, 2 CED with the reducer, 3 CED with the reducer and the transformer

The basic singularities of vibration and acoustic processes at induction motor operation in

systems of CED are that in a different operating points of an observed control range intensity

of all three aforementioned sources largely change, and also resonance appearances are

observed. In this connection it is necessary the reviewing of noise levels and vibrations in all


279

control range for the purpose of their comparison to allowances. Thus it is necessary to

consider that a source strength of a magnetic origin is in many respects defined by a harmonic

composition of voltage feeding motor, i.e. depends on type of the convertor, an aspect of the

regulating used in it, a regime of its operation, the applied law of the frequency control and a

drive loading. System approach according to which all functional indexes, including on

vibration and noise levels, are defined by joint consideration of operation of all builders going

into the drive, allows generating of complex MM of vibration and acoustic processes of CED,

invariant to various convertors and loadings. Account vibration and acoustic indexes of a

magnetic origin taking into account the temporary harmonic voltage can be executed on a

procedure, designed by Shumilov U.A. and Gerasimchuk V. G. [24], according to which forces

of a magnetic origin are divided depending on direction of action into the radial and tangential;

vibrations and noise are defined from these components. The basic assumption is the

conjecture of linearity of a mechanical system at which frequency of magnetic vibrations and

noise is equal to frequency of a magnetic force causes it, and the amplitude of deformations is

computed by division of the force operating with given frequency, into rigidity of a

construction (taking into account a reinforcement of deformations at a resonance). The end

result of calculations is plurality of amplitudes of vibrations on matching frequencies (a

vibration spectrum) and a common level of magnetic noise. At the same time at use of this

procedure in complex MM for calculation of vibration and acoustic indexes of controlled

induction motors it is necessary to consider that in each operating point of a control range

parameters of equivalent circuits of controlled induction motors and EMF sections of the

magnetic circuit of each observed harmonics vary. At such account adequacy offered in MM

[12] raises. As a result vibration and acoustic account are defined following vibrations and

noise parameters: the relative level of vibrations speed Sv and the level of magnetic noise Sn

depending from vibrations speed and the relative radiated power Nrel. Their numerical values in

a various operating point of a control range of induction motor depend on an aspect of a

loading, type of the convertor, an aspect of regulating, the law of the frequency control. At

account geometrical sizes and properties of materials of an induction motor, and also

magnitude of diameters of the core of the stator, the framework, width of a wall of the stator

and the framework, moduluses of materials of the stator and the framework and etc. are used.

The given procedure can be used for definition vibration and acoustic indexes in dynamic

regimes. For this purpose it is necessary to use on each step of the solution of simultaneous

equations variable meanings of electromagnetic and electromechanical magnitudes in vibration

and acoustic calculation.

On Figure 13 rated dependences of vibrations speed Sv=f(t), vibration acceleration Sа=f(t)

and magnetic noise Sn=f(t), ), gained for different motors in the observed CED are presented.

The calculation procedure of ventilating noise of serial induction motors is well completed and

confirmed by experimental data [23]. In induction motors centrifugal fans with various

constructions of vanes are applied. Structural features of vanes is considered by introduction in

initial data of geometrical sizes of used ventilating fans. The relative supply of the ventilating

fan represents a ratio of actual supply of the ventilating fan to the maximum supply and is

defined by aerodynamic efficiency which in turn depends on a construction of vanes of the

centrifugal fan. Level of ventilating noise is defined for various constructions under different

formulas with use of the coefficients which meanings are accepted under tables.

In the induction motors of CED the ventilating fan rotational speed varies over the control

range that stipulates an aerodynamic noise modification. The common level of ventilating

noise depends also on type of the ventilating fan and its constructive sizes.

Level of this noise in the given control ranges on a known procedure can be defined by means

of a program complex for observed alternatives of electric drives [12]. In dynamic regimes

(Figure 14) ventilating noise builds up proportionally to a rotational speed, attaining the

meanings matching to a steady run.


280

The known calculation procedure of mechanical vibrations for usual induction short-

circuited motors [23] is intended for rigid rotors to which rotors of a induction motors of

uniform series refer to.

(а)

(b)

(c)

Figure 13. Vibrations speed (a),vibration acceleration (b) and magnetic noise (c) of motors: 1

CED without the reducer,2 CED with the reducer, 3 CED with the reducer and the transformer


281

Figure 14. Changes of ventilating noise of an induction motor: 1 CED without the reducer, 2

CED with the reducer, 3 CED with the reducer and the transformer

(a)

(b)

Figure 15. Vibrations speed in the radial direction Vr (а) vibrations speed in axial direction Vz

(b) of an induction motor: 1 CED without the reducer, 2 CED with the reducer, 3 CED with

the reducer and the transformer

The causes of mechanical vibrations are the residual unbalance at static both dynamic

balancing of a rotor and presence of rolling-contact bearings. At calculation of vibrations from

rolling-contact bearings it is supposed that on low frequencies the parent of vibrations are an

irregularity of manufacture of the bearing on the principal sizes and inaccuracy of mounting,

and on frequencies above a 3-fold rotational speed - an irregularity of microgeometry of


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bearings, and levels of vibrations are maximum on frequencies of an eigentone of a rotor.

Bearing vibrations have the essential technological spread defined by quality of bearings, and

also a construction and manufacturing methods of motors. Indexes of mechanical vibrations of

controlled induction motors will vary over the control range. They depend on rotor and

machine masses, and also from a rotational speed. The end result of calculation of mechanical

vibrations are: a common level of vibrations speed from imbalance and irregularities of

bearings in the radial direction Vr, a common level vibrations speed from imbalance and

irregularities of bearings in axial direction Vz. The maximum magnitude of indexes of

mechanical vibrations in the given control range in concrete design alternatives can be defined

on a known procedure by means of a designed program complex [12] for comparison of these

alternatives. Magnitude of indexes of mechanical vibrations are defined by gyrating masses of

the propeller and a rotational speed of a curl and irregularities of manufacture of bearings and

inaccuracy of mounting depend on an unbalance.

(a)

(b)

(c)

Figure 16. A modification of mechanical indexes of motors. resultant shaft bending flexure (a)

reduced mechanical stress(b) dynamic carrying capacity of the bearing (c): 1 CED without the

reducer, 2 CED with the reducer, 3 CED with the reducer and the transformer


283

In dynamic regimes (Figure 15) mechanical vibrations build up proportionally to a

rotational speed, attaining the meanings matching to a steady run. Calculations of indexes of

mechanical vibration are executed at the condition of inaccuracy of machining, equalization

and an irregularity of manufacture of bearings an equal 1 micron.

At mechanical calculations of an induction motor in operation steady runs three factors

characterising a mechanical state, - rigidity of the shaft, strength of the shaft and dynamic

weight-lifting capacity of bearings [17, 22] are observed.

For an estimate of a mechanical state of an induction motor at regulating it is offered to

observe the same factors in dynamic modes of operation according to set tachogram.

At shaft calculation on rigidity the mechanical index - resulting bending flexure of a shaft f is

defining. Except the basic bending flexure of the shaft depending on masses of an active steel

of a rotor and a short-circuited winding, the additional bending flexure of the shaft which

meaning is proportional to a motor torque is observed. The shaft bending flexure is called also

by forces of a single-sided magnetic attraction which originate at rotor bias. It is possible to

count magnitudes of a bending flexure of the shaft while motor speed regulating, using in

known algorithm [17, 22] magnitudes of the motor torques, varying throughout a transient

process according to set tachogram. These magnitudes can be gained by consideration of

unsteady electromechanical processes as a result of the solution of the above-stated system of

differential equations. At shaft calculation on strength reduced mechanical stressσ, considering

combined effect of stress of curving and twisting is defined. Using magnitudes of torques of a

motor varying throughout regulating, it is defined reduced mechanical stress at regulating.

Definition of modifications of rated dynamic weight-lifting capacity of bearings Cb at

regulating is carried out analogously taking into account type of the bearing and character of a

motor load. Designed mathematical models are used in the program [12] with which help

examinations of a mechanical state of the motor at regulating have been executed. At the

analysis it is accepted joining of motors with actuating mechanisms by means of elastic

clutches. In examined electrical machines ball-bearings are used. At examinations character of

a loading with moderate jolts is accepted. The overloading coefficient, equal 2,5 for reversible

machines is used. On Figure 16, a, b, c the results of calculation of the mechanical indexes set

forth above are presented accordingly at regulating of motors in observed CED.

4. Conclusion

1. On the basis of modelling of various CED, inclusive reducer and the matching

transformer, which are ensure a demanded control range at a given load, operation of

different motors was investigated, therefore comparison of characteristics of motors in

static and dynamic regimes is carried out, energy, mass and dimension parameters of

electric drives are defined.

2. The carried out investigations give the chance to justify sampling of the best alternative

of the drive depending on the chosen criteria, including measure of active energy losses

cost.

3. Magnitudes of efficiency of motors for a static conditions are approximately equal to

final values of efficiency in transient regimes accordingly tach gram.

4. View overheating characteristics determined by the increase of heating losses in

dynamic mode and the heat capacity of the thermal circuit designs of the motors.

5. Dependences of vibration speed and noise of a magnetic origin for examined motors

place in one order, unlike dependences of vibration acceleration.

6. Ventilating noise of the motor 4А355М12 is much less than noise of two other motors

as it in the core proportionally depends on a rotational speed of the motor shaft.

7. Vibration speed in the radial direction Vr and vibration speed in axial direction Vz the

greatest for the motor 4А250М4 and the least for the motor 4А355М12.

8. The peak value of resultant shaft bending flexure in dynamic regimes for the motor

4А355М12 exceeds, and for two other motors does not exceed a legitimate value (0,1

from magnitude of a stator-to-rotor gap).


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9. For all motors the peak value of reduced mechanical stress of shafts in transient regimes

do not exceed a legitimate value matching to steels of shafts.

10. The peak value of rated dynamic weight-lifting capacity of the bearing in transient

regimes for the motor 4А355М12 exceeds, and for two other motors does not exceed a

legitimate value matching to type of the bearing.

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Viktor Petrushin head of Electric Cars Department, ONPU,65044, Odessa,

Shevchenko av.,1,ONPU,ph.(048)734-8494.

Vladimir Vodichev head of Electromechanical systems with computer

control Department, ONPU, 65044, Odessa, Shevchenko av.,1,ONPU,

Rostislav Yenoktaiev Master of ONPU, 65044, Odessa, Shevchenko av.,1,

ONPU, ph. (097)046-30-70.


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